A Stochastic Production-Inventory Model in a Two-State Production System With Inventory Deterioration, Rework Process, and Backordering

The existing economic production quantity (EPQ) models in imperfect production systems normally assume either deteriorating production processes or deteriorating inventory. In this paper, the two aspects are combined together in a single approach to solve single machine, single product EPQ problem. There are assumed to be two states: 1) in-control and 2) out-of-control state. At the beginning of each production cycle, the production process is in control with a low defective rate. After a certain time period, the production process switches from an in-control to an out-of-control state. As a result, the defect rate increases to another level and more defective items are produced. Defective products are reworked after the normal production process all together but before that they are stored in an inventory, so a corresponding inventory holding cost is generated. Backordering is also considered in this model and products are first used to satisfy the backlog demand in each production run. Three different cases are considered and discussed in which the switch of state occurs in the backlog period, the inventory surplus period, and after the normal production period, respectively. By finding the optimal total production and backlog quantity, the expected total cost per unit product is minimized.